Electronic and Optical Properties of Functionalized GaN (10-10) Surfaces using Hybrid-Density Functionals
Dennis Franke, Michael Lorke, Thomas Frauenheim, Andreia Luisa da Rosa
aa r X i v : . [ c ond - m a t . m t r l - s c i ] O c t Electronic and Optical Properties of Functionalized GaN (10-10) Surfaces usingHybrid-Density Functionals
Dennis Franke, Michael Lorke, and Thomas Frauenheim
Bremen Center for Computational Materials Science,University of Bremen, Am Fallturm 1, 28359 Bremen, Germany
Andreia Luisa da Rosa
Universidade Federal de Goi´as, Campus Samambaia, 74690-900 Goiˆania, Brazil andBremen Center for Computational Materials Science,University of Bremen, Am Fallturm 1, 28359 Bremen, Germany
Adsorption of small ligands on semiconductor surfaces is a possible route to modify these surfacesso that they can be used in biosensing and optoelectronic devices. In this work we perform density-functional theory calculations of electronic and optical properties of small ligands on GaN-(10¯10)surfaces. From the investigated anchor groups we show that thiol groups introduce states into theGaN band gap. However, these state are not optically active, at least for these perfect surfaces.This means that more realistic surfaces need to be considered to suggest how surface modificationcan enhance the optical properties of GaN non-polar surfaces.
I. INTRODUCTION
Scientific interest in hybrid nanostructures consisting of organic and inorganic materials for the fabrication ofelectronic and optoelectronic devices with novel properties has grown over the past years [1, 2]. GaN is a semiconductormaterial with a wide (3.4 eV) band gap widely used in ultraviolet-blue light emitting diodes, photodetectors and lasers[3, 4]. Due to its stability one of the major interest in GaN is for biomedical applications[5–8]. Functionalization withsmall ligands is a possible route to functionalize semiconductor surfaces, since these groups can subsequently bindcovalently to a wide range of biomolecules or even be used to introduce optically active states in the band gap whichare suitable for optoelectronic devices. Several organic groups such as thiols [9], alkenes [10] and silanes[11] havebeen used to modify the surface of GaN. In particular, the adsorption of thiols on GaN surfaces indicates that themolecule adsorbs via the thiol group and remain stable upon annealing [9]. Furthermore, Stine et al. [12] developeda technique to produce amine groups directly on GaN surfaces to successfuly imobilize biomolecules. However, manyaspects regarding suitable groups and their effect on the electronic and optical properties of GaN remain unclear. Inthis work we perform density-functional theory calculations of electronic and optical properties of small ligands onGaN-(10¯10) surfaces as they can be used to imobilize larger organic and bio-molecules or even to modify the GaNsurface to be used in optoelectronic devices. We show that although thiol groups introduce states in the GaN bandgap. However, these state are not optically active. As we consider only perfect surfaces, we suggest that more realisticsurfaces need to be considered to identify possible mechanisms to enhance the optical properties of GaN non-polarsurfaces.
II. COMPUTATIONAL DETAILS
While structural properties such as bond lengths are reliably obtained within the PBE [13, 14] form of the exchange-correlation functional, the electronic structure can be severely underestimated [15, 16]. In particular for GaN, the useof PBE yields a band gap of 2.4 eV, a value which is too small compared to the experiment (3.2-3.4 eV) [17]. It hasbeen shown that the use of hybrid-density functional where an amount of Hartree-Fock exchange is added to the PBEexchange energy term lead to an overall improvement of chemical and physical properties of solids and molecules,specially band gaps [18]. In this work we use the PBE0 form for the exchange correlation functional where 25% ofHartree-Fock exchange is added to the PBE functional [19] to investigate the structural and electronic propertiesof hybrid GaN-organic interfaces. The ground state of GaN is a wurtzite structure with 4 atoms per unit cell. Tomodel the surface, we consider a GaN slab containing 8 GaN layers with a vacuum region of 18 ˚A. We adsorb twomolecules per supercell, one on each side of the slab. Molecules of the form CH − X where X = COOH, SH and NH were adsorbed on the GaN surface with 1 ML (monolayer) coverage. We have used density functional theory (DFT)[20, 21] as implemented in the Vienna ab initio simulation package (VASP) [22, 23]. The projected augmented wave(PAW) method has been employed [24, 25]. The atomic structure was optimized with the PBE functional, while theelectronic and optical properties have been calculated with the PBE0 functional. A plane wave basis with an energycutoff of 400 eV and a (1 × ×
10) Monkhorst-Pack k -point sampling have been used in all calculations. Forces onall atoms hav been converged until they are smaller than 0.001 eV/˚A III. RESULTS
The optimized geometries of functionalized surfaces are shown in Fig. 1. Thiol and carboxyl groups adsorb on thesurface in a dissociative manner, while the amine group does not dissociate. All molecules adsorb in a monodentatebinding mode. The Ga-N bond lengths in the center of the slab are similar to those found in bulk GaN, varyingbetween 1.95 and 2.00 ˚A. This indicates that our slab is large enough to avoid spurious interactions between the twosides of the slab. As the surface is modified with the small molecules, there is a shortening of these bond lengths(1.84-1.90 ˚A) for the − NH group which binds non-dissociatively. On the other hand adorption of -SH and -COOHgroups lead to Ga-N bond lengths close to the bulk values.For thiol groups (left figure) in Fig. 1, the -SH groups adsorbs on the surface via S-Ga bonds with a bond lengthof 2.26 ˚A and an angle of 115 ◦ . The Ga-S-C angle is 111 ◦ . The carboxyl groups (Fig. 1, middle) bind via twoasymmetric bonds between the O atoms of the functional group and the surface Ga atoms with a bond length of 1.90˚A and a binding angle of 120 ◦ . The characteristic O-C-O angle is 122 ◦ . The amine groups adsorb via N-Ga bondswith a resulting bond length of 2.15 ˚A and an angle of 117 ◦ . The Ga-N-C angle is 132 ◦ . The discussed bond lengthsare somewhat similar to the results found in our previous work on functionalized ZnO (10¯10) surfaces [26, 27]. Allgroups bind strongly to the GaN surfaces, which corroborates with previous experimental findings which suggested FIG. 1. Optimized structures of the GaN surface functionalized with CH − SH (left), CH − COOH (middle) and CH − NH (right) molecules. The spheres represent gallium (light pink), nitrogen (blue), oxygen (red), carbon (turquoise), sulfur (yellow)and hydrogen (white) atoms. that these groups are stable on GaN [9, 12].Next we discuss the electronic and optical properties of the functionalized structures. The total density-of-states(DOS) and the projected DOS onto the molecular orbitals for the bare and functionalized surfaces are shown inFig. 2. The band alignment has been done with respect to the vacuum level as described in Refs. [28, 29]. The use ofthe hybrid PBE0 functional significantly improves the band gap of bulk GaN, yielding a value of 3.6 eV, somewhatoverestimated but closer to experiment [17] and in agreement with previous calculations[30]. We then performedfurther electronic structure calculations for the bare and modified surfaces with this functional. Bare surfaces havea slightly reduced band gap compared to bulk value, due to extra surface states appearing close to the valence andconduction bands (i have to check this). Modified surfaces with -SH introduce intra-gap states, mainly due to S- p orbitals. These states are located 0.3 eV and 1 eV above the top of the valence band (VBM), as it can be seen in Fig. 2(b), similarly to what we have found for ZnO surfaces [26]. These state also hybridize with the N- p surface states,but this induces only small changes close to VBM.On the other hand, functionalization with -COOH does not produce intragap states, as shown in Fig. 2 (c) . Instead,surface N- p states hybridize with the O- p of the functional group. This results in states directly at the VBM. The statesassociated with the C- p orbitals are located deep in the valence band and overlap with Ga- d states. Molecular statesappear in the conduction band only at very high energies and stem from C and O p -states. Functionalization with-NH groups does not lead to significant changes in the GaN band structure. The most striking feature is perhapsan overall shift to higher energies compared to the previous systems. This might be explained noticing the non-dissociative binding mode of this molecule. The surface nitrogen atoms are not saturated and thus possess danglingbonds, which strongly reduces the work function of the functionalized system. Our results are in agreement withexperimental findings, which suggested that the formation of amine groups do not significantly alter the conductivityof the GaN substrate[12].The above discussed results on the electronic structure of functionalized GaN surfaces are very similar to earlier -8 -6 -4 -2 0 2 4 6 8Energy [eV] DO S [ a r b . un it s ] totala) bare -8 -6 -4 -2 0 2 4 6 8Energy [eV] DO S [ a r b . un it s ] totalmoleculeb) SH-8 -6 -4 -2 0 2 4 6 8Energy [eV] DO S [ a r b . un it s ] totalmoleculec) COOH -8 -6 -4 -2 0 2 4 6 8Energy [eV] DO S [ a r b . un it s ] totalmoleculed) NH FIG. 2. Projected DOS for the a) bare and functionalized surfaces with b) -SH, c) -COOH and d) -NH groups. The full blackline represents the total DOS, the green region shows the projection onto the ligand states. The dashed lines denotes the Fermienergy. investigations on ZnO surfaces [26, 27]. In order to identify further characteristics and similarities with ZnO, we havecalculated the optical properties of the GaN functionalized surfaces. The dielectric function for these systems is shownin Fig. 3. While for functionalized ZnO the intra-gap states of the thiol group are optically active and lead to anenhancement of the low energetic absorption[26, 27], no such behavior is found for thiol groups on GaN surfaces.This means that such a functionalization would trap holes in the band structure which do not recombine. A similarbehavior is found for -COOH on GaN, where also the presence of the molecular states at the band-edge suppressesthe optical absorption. In contrast, surfaces modified with -NH and bare surfaces show a distinct peak around theabsorption onset, reflecting the presence of dangling bonds. IV. CONCLUSIONS
In summary, we have investigated the structural and electronic properties of GaN surfaces modified by small ligands.We found that the functionalization with carboxilic acids or amine groups does not influence the electronic properties ε || BareSHCOOHNH a) ε p e r p BareSHCOOHNH b) FIG. 3. Dielectric function for the bare and modified surfaces, shown are (a) ε || and (b) ε ⊥ . of these surfaces significantly. Functionalization with thiol groups resulted in the appearance of intra-gap molecularstates. However, in contrast to thiol groups on previously investigated ZnO surfaces[31], these states are not opticallyactive, probably leading to hole trapping. Further investigations on more realistic surfaces including perhaps thepresence of hydroxyl groups and defects are needed to suggest whether and how surface modification can enhance theoptical properties of GaN. V. ACKNOWLEDGEMENT
The authors acknowledge funding by the DFG research group FOR 1616 Dynamics and Interactions of Semicon-ductor Nanowires for Optoelectronics. A. L. Rosa also thanks CNPq and FAPEG for funding.
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